Darboux Transformation of the Green Function for the Dirac Equation with the Generalized Potential

We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions. We also construct the formula for the unabridged trace of the difference of the transformed and the initial Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We illustrate our findings by the consideration of the Darboux transformation for the Green function of the free particle Dirac equation on an interval.Comment: 14 pages,zip. file: Latex, 1 figure. Typos corrected, the figure replace

Elasticity modules and acoustic properties of metal ceramics on the basis of tungsten monocarbide

The results of measurements of acoustic wave speeds and elasticity modules of metal ceramic alloys on the basis of tungsten monocarbide in temperature range of 100...295 K as well as amplitude dependences of internal friction at temperatures 140...295 K and after ?-irradiation (60Со, 1,25 MeV, 5.103 and 105 Gy) have been given. It was shown that elasticity modules of alloys decrease monotonously at increase of cobalt concentration. Radiation influence stimulates the processes complicating movement of grain boundary dislocations in alloys. Representation of these alloys in the form of isotropic mixes of anisotropic phases describes qualitatively correctly the dependence of elasticity modules on structure. The resulted experimental and calculated values of elasticity modules may be used for estimation of elastic and strength properties of these alloy

Historical conditions of human capital’s formation in the higher education’s non-state sector abroad

Private education in most countries is considered as an important part of the national education system. Having a long history private education demonstrates high quality and standards of education. Historical conditions of human capital’s formation in the non-state sector of higher education in foreign countries (China, the UK, the USA, and others) are analyzed. Features of human capital’s formation in the private sector of education in different countries are characterized

Connection between the Green functions of the supersymmetric pair of Dirac Hamiltonians

The Sukumar theorem about the connection between the Green functions of the supersymmetric pair of the Schr\"odinger Hamiltonians is generalized to the case of the supersymmetric pair of the Dirac Hamiltonians.Comment: 12 pages,Latex, no figure

MSSM-inspired multifield inflation

Despite the fact that experimentally with a high degree of statistical significance only a single Standard Model--like Higgs boson is discovered at the LHC, extended Higgs sectors with multiple scalar fields not excluded by combined fits of the data are more preferable theoretically for internally consistent realistic models of particle physics. We analyze the inflationary scenarios which could be induced by the two-Higgs doublet potential of the Minimal Supersymmetric Standard Model (MSSM) where five scalar fields have nonminimal couplings to gravity. Observables following from such MSSM-inspired multifield inflation are calculated and a number of consistent inflationary scenarios are constructed. Cosmological evolution with different initial conditions for the multifield system leads to consequences fully compatible with observational data on the spectral index and the tensor-to-scalar ratio. It is demonstrated that the strong coupling approximation is precise enough to describe such inflationary scenarios.Comment: 27 pages, 4 figures, 5 tables. Version to appear in JHEP. Additions made to the text of the Introduction dealing with the issues of conformity of this multifield model and models of N=1 supergravity (pages 2-3). Added new inflationary scenarios, which are an artifact of such analysis (pages 11-12, Tables 1-4). Additional comments on page 9 and page 13. New references adde

Coherent Schwinger Interaction from Darboux Transformation

The exactly solvable scalar-tensor potential of the four-component Dirac equation has been obtained by the Darboux transformation method. The constructed potential has been interpreted in terms of nucleon-nucleon and Schwinger interactions of neutral particles with lattice sites during their channeling Hamiltonians of a Schwinger type is obtained by means of the Darboux transformation chain. The analitic structure of the Lyapunov function of periodic continuation for each of the Hamiltonians of the family is considered.Comment: 12 pages, Latex, six figures; six sections, one figure adde

On the superstring-inspired quantum correction to the Starobinsky model of inflation

Superstring/M-theory is the theory of quantum gravity that can provide the UV-completion to viable inflation models. We modify the Starobinsky inflation model by adding the Bel-Robinson tensor $T^{\mu\nu\lambda\rho}$ squared term proposed as the leading quantum correction inspired by superstring theory. The $(R+\frac{1}{6m^2}R^2 -\frac{\beta}{8m^6}T^2)$ model under consideration has two parameters: the inflaton mass $m$ and the string-inspired positive parameter $\beta$. We derive the equations of motion in the Friedmann-Lemaitre-Robertson-Walker universe and investigate its solutions. We find the physical bounds on the value of the parameter $\beta$ by demanding the absence of ghosts and consistency of the derived inflationary observables with the measurements of the cosmic microwave background radiation.Comment: 22 pages, 5 figures, LaTe